Suppose that we are collecting a large data set on emotional reactivity in adults. Assume that for most adults emotional reactivity is normally distributed with a mean of 100 and a standard deviation of 10. But for people diagnosed with bipolar disorder, their scores are all over the place. Some are temporarily depressed and they have low reactivity scores. Others are temporarily in a manic phase and their scores are quite high. As a group they still have a mean of 100, but they have a standard deviation of 30. Assume that 10% of the population is bipolar. (The actual percentage is closer to 1%, but 10% will lead to a better example.) This is a case of what is called a mixed normal distribution. Sketch what you think that this distribution might look like. What would happen if we made the means very different?
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